How Do Newton's Laws Apply to a Block and Toboggan on a Frictionless Surface?

[aal0315]

Homework Statement

A 4.0 kg toboggan rests on a frictionless icy surface, and a 2.0 kg block rests on
top of the toboggan. The coefficient of static friction between the block and
the surface of the toboggan is 0.60, whereas the kinetic friction coefficient is
0.51. The block is pulled by a 30 N-horizontal force as shown. What are the
magnitudes and directions of the resulting accelerations of the block and the
toboggan?

Homework Equations

Fnet = F-Ffr = ma
Ffr = μk*Fn

The Attempt at a Solution

I found that the box will move ontop of the toboggan because μs *Fn = 11.76 N which is less than 30 N so the box will move.
F-Ffr = ma
30N - 10.0N = 2.0 kg (a)
accel. = 10 m/s^2
so i know that's the box on the toboggan. How do i find the toboggan on the ground?
do i just do it as
F-Fr = (Mb +Mt) *a
30 - 10 = (2.0 + 4.0) *a
20 = 6.0 *a
a = 3.33m/s^2
does that make sense at all? any help would be great.
thanks

 

[Delphi51]

I agree with your a = 10 for the box.
But isn't the friction force of 10 N the only force on the toboggan? That is the "grip" the pulling system (including the box) has on it. I would apply F = ma to the toboggan with F = 10.

 

[aal0315]

I don't really understand the "grip" pulling system. I don't understand why the F = 10N. wouldn't the toboggan still move in the same direction as the box because 30N is greater than 10N?

 

[aal0315]

can someone please help me with this question? i just need to know if this is right or not or if I am completely wrong and need to start again

 

[slmg_2006]

Have you drawn free body diagrams for these? It might help clear it up if you haven't...

 

[aal0315]

well I am not sure about the FBD of the toboggan. i figured out the block one though. The above calcuations for the toboggan that i did i guess is not right?
i figured that there would still be the force of 30N west and the force of friction against it, so the total force is 20N west.
is the above correct?

 

[slmg_2006]

The 30N are only working on the block... what is pulling the toboggon forward?

 

[Delphi51]

Block: - Friction + 30 = m*a
Toboggan: Friction = m*b (where b is the acceleration of the tobagan)
Friction = .51*2*g = 10
so the block accelerates at 10 m/s^2 and the toboggan accelerates at 2.5.

 

[aal0315]

does that mean that the toboggan is moving east and the block is moving west? because i need to find the directions of the accelerations as well.

 

[Delphi51]

Both move the same way. The way the 30 N pull is exerted. You haven't said which way that is.

 

[slmg_2006]

I answer your question with a question of my own:
What way is the friction between the box and the toboggon acting on the toboggon?

 

[aal0315]

i guess the friction between the box and toboggan will act in the opposite direction on the toboggan and ground?
little confused.
how do i find the directions of the accelerations?

 

[Delphi51]

The ground is not involved - frictionless.
The friction between the box and the toboggan acts one way on the box and the other way on the toboggan. It opposes the motion of the box and causes the motion of the toboggan.

 

[slmg_2006]

delphi is right, accel would be in the same direction of friction because the ground is frictionless...

 

[aal0315]

ok so let me just sure i have this right
accel box = 10m/s^2 to the left
accel toboggan = 2.5 m/s^2 to the left?

 

[slmg_2006]

*friction acting on the toboggon

 

[slmg_2006]

yes, you would be correct

 

[aal0315]

thank you for the help )